We have established the average shape and location of Mercury's magnetopause and bow shock from orbital observations by the MESSENGER Magnetometer. We fit empirical models to midpoints of boundary crossings and probability density maps of the magnetopause and bow shock positions. The magnetopause was fit by a surface for which the position R from the planetary dipole varies as [1 + cos(θ)]−α, where θ is the angle between R and the dipole-Sun line, the subsolar standoff distance Rss is 1.45 RM (where RM is Mercury's radius), and the flaring parameter α = 0.5. The average magnetopause shape and location were determined under a mean solar wind ram pressure PRam of 14.3 nPa. The best fit bow shock shape established under an average Alfvén Mach number (MA) of 6.6 is described by a hyperboloid having Rss = 1.96 RM and an eccentricity of 1.02. These boundaries move as PRam and MA vary, but their shapes remain unchanged. The magnetopause Rss varies from 1.55 to 1.35 RM for PRam in the range of 8.8–21.6 nPa. The bow shock Rss varies from 2.29 to 1.89 RM for MA in the range of 4.12–11.8. The boundaries are well approximated by figures of revolution. Additional quantifiable effects of the interplanetary magnetic field are masked by the large dynamic variability of these boundaries. The magnetotail surface is nearly cylindrical, with a radius of ~2.7 RM at a distance of 3 RM downstream of Mercury. By comparison, Earth's magnetotail flaring continues until a downstream distance of ~10 Rss.